Assignment:
Q1. Write the following in expanded for then find the sum
a) ^7(Sigma sign) k=0 (k=1)(k+2)
b) ^7(Sigma sign) k=4 3k
Note: The sigma sign does not show up when pasted here. The 7 is on top of the sigma sign and the k= 0 or k=2, respectively, lies below the sigma sign.
Q2. Express the following series using sigma notation:
a) (1 X 0)/2 + (2 X 1)/3 + (3 X 2)/4 + ........ (10 X 9)/11
b) (1 X 2)/2 + (2 X 3)/4 + (3 X 4)/6 + .......... (8 X 9)/16
Q3. Use the Binomial Theorem to expand the following equation:
a) (2p - 3q)^4
b) (2p + 1)^4
Q4. Find the fifth term in the expansion of (4x + 2y)^7
Q5. Find the sum of the following series, or state that the sum does not exist
a) 12 + 8 + 16/3 + .......
b) 1/12 + 1/2 + 3 + .........
Q6. Find the limit of the following or state that the limit does not exist
a) (2n - 1)/n^3
b) ......as n approches infinity of (2n^2)/(n^2 - 1)
Provide complete and step by step solution for the question and show calculations and use formulas.